Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 12The column labeled Population gives the population parameter valuesthat are given in the MODEL command, the MODEL COVERAGEcommand, or using the COVERAGE option of the MONTECARLOcommand. The column labeled Average gives the average of theparameter estimates across the replications of the Monte Carlosimulation study. These two values are used to evaluate parameter bias.To determine the percentage of parameter bias, subtract the populationparameter value from the average parameter value, divide this number bythe population parameter value, and multiply by 100. The parameterbias for the variance of i would be100 (.4820 - .5000) / .5000 = -3.6.This results in a bias of -3.6 percent.The column labeled Std. Dev. gives the standard deviation of theparameter estimates across the replications of the Monte Carlosimulation study. When the number of replications is large, this isconsidered to be the population standard error. The column labeled S.E.Average gives the average of the estimated standard errors acrossreplications of the Monte Carlo simulation study. To determine standarderror bias, subtract the population standard error value from the averagestandard error value, divide this number by the population standard errorvalue, and multiply by 100.The column labeled M.S.E. gives the mean square error for eachparameter. M.S.E. is equal to the variance of the estimates across thereplications plus the square of the bias. The column labeled 95% Covergives the proportion of replications for which the 95% confidenceinterval contains the population parameter value. This gives thecoverage which indicates how well the parameters and their standarderrors are estimated. In this output, all coverage values are close to thecorrect value of 0.95.The column labeled % Sig Coeff gives the proportion of replications forwhich the null hypothesis that a parameter is equal to zero is rejected atthe .05 level (two-tailed test with a critical value of 1.96). The statisticaltest is the ratio of the parameter estimate to its standard error, anapproximately normally distributed quantity (z-score) in large samples.For parameters with population values different from zero, this value isan estimate of power with respect to a single parameter, that is, the364